Question

Helium, a monatomic gas, is initially at a pressure of 15 atm, a volume of 1.1 L, and a temperature of 588 K. It is quasi-statically expanded at constant temperature until its volume is 3.9 L, and is then quasi-statically compressed at constant pressure until its volume and temperature are such that a quasi-static adiabatic compression will return the gas to its original state.

(b) Find the volume and temperature after the compression at constant pressure

volume______	L
temperature ____	K

(c) Find the work done during each cycle.
____ atm · L

(d) Find the efficiency of the cycle.
_____ %

Answer 1

Refer the figure above:

Since it is a monoatomic gas, we know that

Also, considering ideal gas equation is given by:

...EQ1

It is given pressure at A,

Temperature at A,

Volume at A,

using EQ1 we get

...........EQ2

Since AB is isothermal process so

Volume at B is

for isothermal process , we have

Since there is expansion in AB process work is positive (work done by system) is given by:

Also, this work is done by adding heat (positive), so heat transfer for AB will be:

The process BC is isobaric process, then

The process CA is adiabatic process, then

The process BC is isobaric, then

work is negative as it is compression and work is done on the system.

Also, for Monoatomic gas we have specific heat capacity at constant pressure given by:

.......EQ3

Heat transfer in process BC (using EQ3) will be:

Using EQ2 we get

Negative sign means heat is released in the process.

For adiabatic process CA,

and work done in process CA will be:

So total work,

part B

Volume and Temperature after the isobaric compression,

PART C

PART D